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HANDWRITING 






By EDWARD L. THORNDIKE 

tl 



Professor of Educational Psychology, Teachers College 
Columbia University 



Reprinted from Teachers College Record, Vol. It, No. 2, March 1910. 



PUBLISHED BY 

Gfeartpra (&o\U$t, (Mmtttoa Itttiwrutti} 

NEW YORK CITY 

1912 






Copyright 1910 
Copyright 1912 



CCI.A314733 
^0 I 



CONTENTS 

SECTION PAGE 

i. Introduction i 

Part I. The Measurement of the Quality of Handwriting 

2. The Construction of a Scale for Quality of Handwritings by 

Children in Grades 5 to 8 4 

3. The Nature of the Scale, including Qualities or Degrees of Merit 

from that of Copy-Book Models down 7 

4. Criticisms of the Scale 8 

5. The Uses of the Scale 17 

6. A Scale for Quality in Adult Women's Writing 19 

7. The Derivation of the Scale 24 

Part II. The Speed and Quality of Handwriting in 
Seven School Systems 

8. Differences between Systems 29 

9. The Relation of Differences in Results to Differences in Means 

and Methods of Teaching Handwriting 32 

10. Differences between Individuals within the Same School System.. 33 

11. The Relation Amongst Individuals between Speed and Quality. . 35 

12. The Relation of the Quality of Slow Writing to the Quality of 

Rapid Writing by the Same Individual 36 

13. Miscellaneous Comments 36 

14. A Scale Based on Equally Often Noted Differences in Quality. . . 40 

Scale A between pp. 10 and 11 

Scale B " " 24 and 25 

Scale C " " 40 and 41 



HANDWRITING OF CHILDREN IN GRADES S 



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HANDWRITING 

Section i. Introduction 

Handwriting may profitably be studied from three points of 
view:— that of the physiology and psychology of movement, 1 
that of the part it may play in the intelligently directed activities 
of child life in schools, 2 and that of the direct examination of 
the quality and speed of handwriting secured by various forms 
of school training. But to any study of it there is one very 
desirable preliminary — some means of measuring the quality 
of a sample of handwriting. 

At present we can do no better than estimate a handwriting 
as very bad, bad, good, very good, or extremely good, knowing 
only vaguely what we mean thereby, running the risk of shift 
ing our standards with time, and only by chance meaning the 
same by a word as some other student of the facts means by 
We are in the condition in which students of temperature were 
before the discovery of the thermometer or any other scale for 
measuring temperature beyond the very hot. hot. warm, luke- 
warm, and the like, of subjective opinion. ^vVe opine roughly 
that, at a fairly rapid rate, writing-movements in which the fore- 
arm shares will produce a better quality of handwriting than 
movements confined more exclusively to the thumb and fingers, 
but no one could estimate with surety and precision how much 
better the best rapid " free-arm " writing is than the best equally 
rapid " finger-movement " writing. We opine roughly that drills 
in which good writing serves some end of consequence to the 

1 No attempt is made in this article to report any results of physio- 
logical or psychological analysis of the behavior involved in hand- 
writing. The student of this aspect of the subject should consult 
especially the investigations of Preyer, Judd and Freeman. 

2 No attempt is made in this article to report the experiences or 
opinions of students of education with respect to the Utilization of 
the original tendencies of children so as to secure a rational and 
economical cultivation of handwriting as an expressive art. 

I 



iJff 



2 Handwriting 

children will be more efficient than drills for mere penmanship, 
but no one could estimate how much more efficient they will be. 
We know that some schools secure better writing at a given 
speed than do other schools, but no one could tell how much 
better in any terms sure of understanding aM(L agreement ; for 
we have no scale to measure handwriting by/&$NV> pupil, teacher, 
or superintendent of schools knows how well any child, class, 
or group of children writes in anything approaching the sense 
in which we know how hot any liquid is or how long a wire is. 

The main purposes of this monograph are to describe the 
means by which a graphometer or scale for handwriting may be 
made, to present such a scale for the handwriting of children 
in grades 5, 6, 7, and 8, to explain how such a scale is to be 
used, to present a similar scale for adult women's handwriting, 
and to mention some of the facts and questions of importance 
to which the discovery and use of these scales have led. 

Many circumstances have combined to prevent me from giving 
at this time anything like a perfect scale. The individual differ- 
ences amongst competent judges in rating any example are so 
great that to get for it a measure accurate within one per cent of 
the difference in merit between the best and the worst of gram- 
mar-school (i.e., grades 5 to 8) writing requires that at least 200 
judges rate it. I have not been able to command the services 
of so many. For the greatest practical convenience a scale 
should have for any quality samples of all the common styles 
of children's writings, and should include about ten qualities 
differing each from the next by equal steps — equal, that is, 
within, say, four per cent of a step or one half of one per 
cent of the difference between the worst and the best grammar- 
school writing. But to get such samples one would need to have 
several thousand samples of each style of writing, and to have 
about half a million ratings made. This means roughly four 
thousand hours of labor. The final selections of samples for 
the scale should properly be made from very many printed 
reproductions such as will form the scale itself. The cost has 
prohibited me from making many of these. 

Tke" v scaie is presented now, in spite of its imperfections, for 
these reasons : It is the result of some twenty thousand ratings 



Introduction 3 

and ensures measurements far more accurate than anyone could 
make without it. For the present needs of school practice 
and educational research, a very precise instrument for measur- 
ing handwriting is not required. The best way to get a more 
perfect scale is by the use of this one as a starting point. , 

This scale is then offered as a preliminary scale whose imper- 
fections the maker is, perhaps, more conscious of than any critic 
will be. I beg the reader to bear this in mind, since, for the 
sake of simplicity in description in what follows, I shall not in 
each case state the fact that a quality or point on the scale is 
determined only to a certain approximation, and the fact that the 
differences between successive qualities are only approximately 
equal. 



PART I 

The Measurement of the Quality of Handwriting 

Section 2. The Construction of a Scale for Quality of Hand- 
writings of Children in Grades 5 to 8 

If one selects from children's written work 1000 samples rang- 
ing from the best to the worst handwriting found in grades 5 
to 8 and tries to rank these 1000 samples in order of merit for 
handwriting, one finds that he cannot make 1000 such ranks. 
Some of the handwritings will be indistinguishable in " good- 
ness " or " quality " or " merit." Nor can one make 100 such 
ranks. Nor can one make 40. One can make about 20, but if 
he so ranks the samples a number of times he gets substantially 
the same average result as he gets when he ranks them a number 
of times in 10 or 11 groups. To get an individual's judgment 
of the relative merits of the 1000 samples it is sufficient to have 
him rank them in 10 or 11 groups three or four times. If he 
grades in 10 groups and tries to make the difference in 
" goodness " or " quality " or " merit " all equal, — to make, that 
is, the sample he puts in the highest group (call it 11) as much 
superior to those in the next highest group (call it 10) as the 
latter are to those he puts in the second from the highest group 
(call it 9), etc., etc., — we have in the average 1 result of his 
groupings his judgment of the relative merits of the samples in 
a specially convenient form. For instance, if he grades sample 
217 as in group 5 three times, as in group 4 once, and as in 
group 6 once, and grades sample 218 as in group 6 three times, 
in group 5 once, and in group 7 once, he judges 218 to be " 1 " 
better than 217, " 1 " being, in the individual's judgment, one 
tenth of the difference between group 1 and group 1 1. 

If thirty or forty individuals chosen from competent judges 
of handwriting thus judge the 1000 samples, the average 1 of all 



1 Except for certain factors which will be described in section 7. 
4 



The Measurement of the Quality of Handwriting 5 

their gradings give approximately the relative merit of each 
sample in the judgment of competent judges in general. If 
they grade sample 317 in group 3 two times, in group 4 five 
times, in group 5 thirteen times, in group 6 thirteen times, in 
group 7 five times, and in group 8 two times, their average or 
median grade for it is 5.5. If their average or median grade 
for sample 318 is 6.4, they esteem 318 as .9 better than 317. 
The .9 means, in their judgment, nine tenths of one tenth of the 
difference between grade one and grade eleven. 

If now from all the 1000 samples we could find some which 
were graded exactly 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 by the 
average or median 1 judgment of 30 or 40 competent judges, each 
grading the set into groups 1 to 11 by what he thinks are equal 
steps in merit, we would have a very useful scale of merit in 
handwriting. It would include all grades from the worst to 
the best and would proceed by what were, by the average com- 
petent opinion, equal steps. Or if we could find some graded 
1.5, 2.4, 3.3, 4.2, 5.1, 6.0, 6.9, 7.8, 8.7, 9.6, and 10.5 we would 
have a scale nearly as useful. It would not be so likely to in- 
clude the very worst and very best samples, but would proceed 
by equal steps, as before. 

The scale which I shall proceed to describe was obtained by a 
method in principle the same as the above. 

Such a scale could be got in a different way, as follows : Sup- 
pose competent judges to compare each sample with every other, 
stating in each case which was better. If then we picked out 
samples a, b, c, d, etc., such that a was judged better than b, 
just as often as b was judged better than c, and just as often as 
c was judged better than d, and so on, we could have, in samples 
a, b, c, d, etc., a scale by equal steps, if two other conditions were 
fulfilled by them. The first of these conditions would be that a 
should not be judged better than b and worse than b equally 
often. For if it were, a would be equal to b, b to c, c to d, and 
so on, and we would have no extent to our scale. The second 
of these conditions would be that a should not always be judged 
better than b. For, if it were, it might be just enough better 
to barely be so judged, or it might be very, very much better. 



1 Except for certain factors which will he described in section 7. 



6 Handwriting 

Only if differences are not always noticed can we say that dif- 
ferences equally often noticed are equal. But if we had, as 
a result of the judgments, facts like those below, we could say 
that a, b, c, d, etc., represented samples of writing progressing 
by equal steps of difference in quality. 

iooo comparisons of a, b, c, d, etc., being made : 

a was judged better than b in 73 per cent., equal to & in 11 
per cent., and worse than b in 16 per cent, of the judgments. 

b was judged better than c in 73 per cent., equal to c in 11 
per cent., and worse than c in 16 per cent, of the judgments. 

c was judged better than d in 73 per cent., equal to b in 11 
per cent., and worse than b in 16 per cent, of the judgments, and 
so on for d-e, e-j, n. 

The scale which I shall describe was tested throughout by this 
second method. The two methods do not give results that corre- 
spond exactly. The variations follow this rule: Judges will 
notice differences between poor samples when they compare 
them directly one with another which they would not count in 
rating them by a mental scale. For example, suppose samples 
a, b, c, and d to be rated 10, 9, 3, and 2 by comparison with a 
mental scale of eleven grades by equal steps. The percentage 
of judges regarding 10 as better than 9 will be smaller than that 
regarding 3 as better than 2. 

Since we get two different scales by the two methods, there 
are four alternatives. We may adopt one or the other or com- 
bine them, or give the results by both methods. I shall take 
the latter alternative, but shall at this point present only the scale 
as derived by the first method. In a later section (Section 12) 
the scale is derived by the second method will be presented. 

The scale given here is then a scale in which the steps of dif- 
ference are equal in the sense of being called equal by competent 
judges. Equal will mean just this in the next three sections. 
They are not equal in the sense of being equally often noticed 
when the single question " better or worse," is answered for 
each sample in connection with every other sample. The dif- 
ferences in the upper part of the scale would be less often so 
noticed than those in its lowest third. 



The Measurement of the Quality of Handwriting 7 

Section 3. The Nature of the Scale 

Scale A is the scale for merit of the handwriting of children 
of grades 5 to 8. It is not a scale of merit of the writings of 
children of grades 1 to 4 or of the writings of boys and girls of 
high-school age. It can, however, be more or less well used 
for such cases until we get more appropriate scales. Each set 
of samples represents a point on this scale. 

The use of 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17 for these 
qualities of handwriting means, first of all, that 14 is as much 
better than 13, as 13 is than 12; that 13 is as much better than 12, 
as 12 is than 11, and so on. In the second place it means that 
quality 14 is two times as far above o merit in handwriting as 
quality 7 is; that quality 16 is twice as far above o merit in hand- 
writing as quality 8 is, and so on. Zero merit is defined roughly 
as writing as bad as sample 140 (see page 16), as a hand- 
writing, recognizable as such, but of absolutely no merit as hand- 
writing. The use of several samples under one quality means 
that those samples are of equal merit. The scale includes sam- 
ples of as many different styles as could be obtained, so that in 
using the scale the merit of any sample of any style of writing 
can be quickly ascertained by comparison with the scale. The 
scale extends in actual samples by children from nearly the 
worst writing 1 of fourth-grade children (quality 5) to nearly the 
best writing of eighth-grade children (quality 17). Quality 7 is 
nearly the worst writing of fifth-grade children. 

The scale includes a sample of a copy-book model which is 
rated by competent judges as of approximately quality 18, two 
samples of fourth-grade writing which are judged to be approxi- 
mately of qualities 6 and 5, and a very bad writing, arti- 
ficially produced, which is rated by competent judges as of ap- 
proximately quality 4. The scale thus extends from a quality 
better than which no pupil is expected to produce, down to a 
quality so bad as to be intolerable, and probably almost never 
found, in school practice in the grammar grades. 

If one had a finer scale, its use would give but slightly more 
accurate results, and would require more practice and more time. 



1 In a formal exercise in writing at their " natural " rate. 



8 Handwriting 

Any specimen of handwriting is measured by this scale by put- 
ting it alongside the scale, as it were, and seeing to what point on 
the scale it is nearest. Thus, the sample on page 9 (sample 9) is 
measured by comparing it with those of Scale A. I judge it to be 
between quality 15 and quality 14 and assign it the measure 14 
rather than any other unit measure of the scale. If one wishes to 
measure more finely than to units, he can add or subtract a frac- 
tion according as the sample to be measured seems better or 
worse than the quality of the scale to which it is nearest. 

The sample to be measured should, for convenience, be exam- 
ined with the entire scale in view. If the scale's samples are 
arranged in order on a table or against a wall, the examined 
sample is easily compared with them. The measurer then de- 
cides what quality of the scale the sample possesses and records 
the measure. The measurer should be, of course, careful not to 
decide its grade because of its likeness in style, but only because 
of its likeness in quality to some sample of the scale. If, for 
instance, one has a pronounced vertical that is really of quality 7, 
one must not call it quality 8, because it is in style more like sam- 
ple 14 than like the sample of quality 7. The measure may be 
made more and more accurate by having other judges also 
measure, each always in ignorance of the ratings given by the 
others. In default of other judges, the measure may be made 
more accurate by rating the sample two or more times, each time 
in ignorance of the ratings previously given. An individual may 
be measured more accurately by using several samples of his 
writing, each being rated in ignorance of the ratings given to the 
other sample. 

Section 4. Criticisms of the Scale 

The scale has, as previously noted, some defects. First of all, 
not all styles of writing are represented on the scale, much less at 
each point of quality on it. For example, we have no pronounced 
backhand writings of certain qualities and no very pronounced 
forward slant of certain qualities. There are hardly any mark- 
edly angular writings on the scale. This defect can be at any 
time remedied by securing enough samples of children's writing 
of the missing sorts at approximately the qualities in question, 



The Measurement of the Quality of Handwriting g 



1 



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io Handwriting 

selecting, with the aid of thirty or forty competent judges, sam- 
ples whose merit is exactly 8 or io or 12 or 14 as the case may 
be, and adding these to the scale. I shall be grateful to any one 
who sends me collections of children's handwritings of styles not 
represented in the scale. 

Each such sample should be accompanied by a statement of all 
the grades assigned to it on our scale by at least ten or twelve 
competent observers, each of whom measures it with the scale 
and rates it in complete ignorance of the ratings given by all the 
other judges. It is desirable, though not necessary, that the 
writings be on unruled paper. 

In the second place, the qualities below 5 and above 17 should 
perhaps be represented in the scale by actual children's writings. 
This defect could be remedied by collecting children's handwrit- 
ings that were superlatively bad and superlatively good. I shall 
be grateful to anyone who sends me samples of children's writing 
which are notably better than quality 17 or notably worse than 
quality 5. 

In the third place, although I have so far spoken of the quali- 
ties 5, 6, 7, 8, 9, 10, etc., as if they might be absolutely these 
amounts — as if the 13's might be all absolutely equal in merit and 
all absolutely halfway between any one of the 12's and any one 
of the 14's — this is not exactly the case. As was noted on page 
3, the scale is only approximate. 16 on the scale does not 
pretend to mean 16.00000, but between 15.9 and 16.1. 8 does not 
pretend to mean 8.0, but between 7.9 and 8.1. And as a matter 
of fact, although I have had a thousand samples graded and have 
chosen as wisely as I could, some of the samples do vary in merit 
from 7, 8, 9, 10, etc., by more than .1 plus or minus. Even after 
one has picked samples that vary only that much, the relations 
may be altered in the process of making the electrotypes from 
which the scale is printed or in the process of printing itself. 
This defect can be remedied by the expenditure of enough time 
and money in getting more samples, having them graded by more 
judges, reproducing more of them in electrotypes, and having 
these reproductions graded again by more judges. In this work 
I am now engaged. The defect is, however, of little consequence 
to any use to which any of my readers is likely to put the scale. 



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The Measurement of the Quality of Handwriting n 

For the variations in the scale are trivial compared to the vari- 
ations in individual judgment. I have measured the quality of 
each sample in the scale to tenths of a step, subject to slight 
changes had more judges been available, and apart from varia- 
tions in the printing. For example, the quality of sample 49 
in the scale is 15.1, not exactly 15.0. 

Similar figures for each sample in the scale are given below. 
If any one wishes to have the values of each sample as precise 
as possible he may substitute these values. In scientific studies 
of handwriting in schools this should be done, but in practical 
grading by teachers the 5, 6, 7, 8, etc., of the scale may be kept 
without the decimal alterations. 

What changes might be made in the qualities, if the consensus 
of thousands of judges were to replace the consensus of from 
twenty to seventy, is shown in the figures in the third column, 
which give the probable average divergences of the former con- 
sensus from the latter. They show that the scale is not nearly so 
precise as, say, a 25 cent scale for weight. But, on the other 
hand, the superiority of the scale to the personal opinion of any 
one teacher or investigator is enormous. The latter would have a 
probable average divergence of from 1.0 to 1.6 from the con- 
sensus of a thousand competent judges. 



Table I 



im -le 


Quality 




32 


16. 1 


• 14 


84 


l6.2 


• 43 


47 


I5.0 


.19 


49 


15. 1 


.18 


89 


I5.0 


• 39 


90 


15. 1 


•35 


19 


I4.O 


.20 


54 


14.0 


.19 


4 


12.9 


.20 


24 


13. 1 


.18 


26 


12. Q 


.18 


55 


13. 1 


.21 


30 


11. 9 


.19 


7 


12.0 


.20 


52 


12.0 


.20 


23 


ir.o 


.20 



Probable average divergence of the 
estimated quality from an estimate 
by an infinite number of judges 



12 Handwriting 

Probable average divergence of the 
estimated quality from an estimate 
by an infinite number of judges 
Sample Quality 

45 II. o .19 

106 11. o .28 

17 10.2 .18 

21 9.1 .15 

28 8.9 .15 

31 8.9 .14 

48 8.0 .14 

14 8.1 .19 

126 7.0 .40 

The reader, in examining the scale, may think that some of the 
samples called equal are really unequal. If he objects to vertical 
writing, he may, for instance, think that sample 55 in Scale A is 
at least one step worse than sample 24. Such criticisms 
of the scale are, however, really strong arguments in its 
favor. For such a critic is surely wrong. That he denies the 
correctness of the average opinion of forty competent judges 
me s simply that his own judgment is partial or crude, and 
the act that each individual's judgments of handwriting are 
thus partial and crude proves that he needs a scale representing 
the general judgment of competent people to help him to judge 
and to teach him to eliminate the unfairness in his own future 
judgments. If no one felt any disagreement with this scale, it 
would not be so valuable as it is under the condition that many 
individuals will think it wrong. For those who are unfair to 
any style of handwriting or who overemphasize beauty in com- 
parison with legibility, or evenness in comparison with " char- 
acter," or the reverse, can be proved by the scale to be unfair — 
that is, to diverge from the average judgment of competent 
people in general. If they are intelligent, they can learn from 
the scale to correct their bias. 

It is possible, however, that some critic may deny the value of 
the average judgment of competent people in general and declare 
that though that judgment pronounces two handwritings equal 
in merit, he knows that they are not equal. Now conceivably he 
might be right. But the chances are enormously against his 
being right, and science naturally cannot count his assurance as 
of more weight than that of any other judge of equal competence. 



The Measurement of the Quality of Handwriting 13 

Some more sophisticated critic may object, not that he knows 
that this scale is wrong and prefers his own supposed competence 
to that of forty of his peers, but that no one can know whether 
this or any such scale is right. For, he will add, any such scale 
is subjective, 1 representing only what certain individuals think 
about the merit or value of samples of handwriting. In this there 
is some truth. There is no value in average opinion as such. 
The world was as round, when the most competent judges 
thought it flat, as it is today. If it should some time be proved 
that evenness of width of line was the sole criterion of real merit 
in handwriting, the scale would be wrong. But in the case of 
handwriting the only available criterion of real " merit " or 
" quality " or " goodness " is the average judgment of competent 
people. A hundred years from now merit in handwriting may 
mean something different from what it now means and a new 
scale may be required. But what it then means will then be 
determined by the average judgment of competent men and 
shown in a scale derived just as this one has been derived. Wnat 
merit does now mean is precisely the thing measured by is 
scale. Merit in handwriting in the judgment of competent 
people today is the composite of qualities, each duly weighted, 
wherein the samples marked 12 are as much better than the 
samples marked 10 as the latter are than those marked 8, etc. 
The scale measures not only some absolute merit, but merit as 
now defined in the average judgment of forty or more persons 
chosen at random from the competent. And no other sort of 
merit is so well fitted to be the basis of a scale. 

A far more sagacious criticism than either of these would be 
that a scale like this for merit in general is less useful than a 
scale for legibility alone, or for beauty alone, or for "character" 
alone, or for ease alone. Of course, I admit that such specialized 
scales are highly desirable, and I hope that this scale for general 



1 If this report were addressed to students specially interested in logic 
and scientific methods applied to the social sciences, it would be worth 
while to show here that the objectivity of a scale for length as compared 
with the subjectivity of a scale for merit of handwritings, Or moral worth 
of acts, or beauty of poems, means only a closer likeness amongst men 
in their judgments, not a radically different sort of judgment. Being 
far, far more alike in sense-organs and muscles than in the central eon 
nections of neurones, we agree far better in comparing lines and weights 
than in comparing handwritings or poems. 



14 Handwriting 

merit will stimulate others to the labor of making similar scales 
for legibility alone, beauty alone, and so on. But it seems sure 
that the scale of most importance and usefulness is that for gen- 
eral merit. General merit is that for which school grades are 
oftenest given, in respect to which school systems or classes are 
oftenest compared, and with which other features of a pupil's 
achievements are oftenest related. Moreover, only after a scale 
for general merit has been made can one measure the extent to 
which legibility, beauty, etc., respectively determine general 
merit. 

So much for criticism of the general method of constructing 
the scale. I turn now to possible criticisms of the scaling itself. 

Some one may ask why 4, 5, 6, 7, 8, etc., are used as the values 
of the samples of Scale A instead of some other equal-step 
series of numbers such as 1, 2, 3, 4, 5, 6, etc., or 65, 67^2, 75, 
77%, 80, etc. The step is made 1 rather than 2% because one 
cannot judge samples precisely enough to profit by more than 18 
divisions in a scale. Hence the time spent in deciding whether 
to call a sample measured by the scale 78 or 76 or jy and in later 
computing with the large numbers would be largely wasted. The 
ratio of the highest to the lowest children's writing in the scale is 
made 17 to 5 (or roughly 3^2 to 1), instead of 6 to 1 or 13 to 9 
(97% to &7%) because, from the average opinion of competent 
judges and the facts of individual differences in motor ability, 
zeal for handwriting, and other factors determining the quality 
of a pupil's writing, the best writing from children in these 
grades seems likely to possess less than six times as much merit 
as the worst, but more than one and a third times as much — in 
other words, to be less than six times as far, but more than twice 
as far, beyond zero merit. 

That is, the scale was arranged so that the numbers represent- 
ing the distances beyond zero of the best and worst samples of 
children's writing in our scale should stand in the ratio of ap- 
proximately 3^2 to 1, and also so that the numbers on the 
scale should be the smallest compatible with as accurate measure- 
ment of handwritings as educational theory and practice need. If 

any one prefers as a scaling 15, 17, 19, 21 43, or 3, 4, 5, 6 

.... 17, or 7, 8, 9, 10. . . .21, it would be hard to prove to him 
that his choice was inferior to the 4, 5, 6, 7, 8. ... 18 used. The 



The Measurement of the Quality of Handwriting 15 

essential thing is that the steps be equal, and that the ratio which 
the amount attached to the best children's writing bears to the 
amount attached to the worst be a reasonable one. 

Having defined what was meant by o merit (see sample 140 on 
page 16, I judged as best I could the distance of sample 141 1 
therefrom in terms of the distance of sample 2 2 therefrom. The 
judgment of 3 2/5 times is by no means final. Indeed I am now 
engaged in an investigation aiming to revise it. I could argue 
plausibly for a ratio as low as 2^ to 1 or for one as high as 5 
to 1. But a ratio somewhere between 3 to 1 and 3^2 to 1 
seems the most reasonable. 

The whole matter of the choice of an absolute o for merit in 
handwriting, and of the consequent absolute values of the points 
on the scale, is one involving many intricate considerations out of 
place in this discussion. I fear that in touching upon it at all I 
may have perplexed some readers. Such may rest confident that 
in using the 4, 5, 6, 7, 8, 9, 10, 11, 12, etc., of the scale in measur- 
ing a sample of handwriting as they would use 4, 5, 6, 7, 8, 9, 
10, 11, 12, etc., dollars in measuring the value of a book or a 
jewel or a trunk, they will commit no error of much consequence 
or, at least, no error so great as they would be likely to commit 
by measuring it in any other one way. 

Another criticism may be that the scale does not guarantee 
agreement among the observers using it to measure a sample of 
handwriting. The same sample may, it will be said, be measured 
by one person as equal in merit to 8, by another as equal to 10, 
and by still another as equal to 9. This is true, but it is not the 
fault of the scale. Observers will disagree in their measure- 
ments made with the scale, but not nearly so much as in meas- 
urements made without it. No scale guarantees absolute agree- 
ment. Observers measuring the length of this line to 

tenths of a millimeter will not agree. But they will agree better 
than they would if they had no scale and judged its length as a 
savage might. 



1 Nearly the best sample from children in grades 7 and 8. 

2 Nearly the worst sample from children in grades 4 and 5. 



i6 



Handwriting 






.t: cj 

ha O 



fl.8 



The Measurement of the Quality of Handwriting ly 

* 
Section 5. The Uses of the Scale 

The topic of this section is fitly treated in the one statement: 
Any measurement of the quality of handwriting may be made 
more accurately and conveniently with the scale, either actually 
present or held in memory, than without it. The reader may 
apply this statement to whatever cases his interests suggest. I 
shall mention a few of the commoner uses and explain the func- 
tion of the scale as a standard held in memory. 

The class-room teacher has to measure the quality of a single 
pupil's handwriting in order to assign him a rating in comparison 
with his fellows and, better still, in comparison with his own past 
performances. If she uses the scale either by giving its numeri- 
cal measures outright or by letting her A, B, C's, or 75, 80, 82, 
etc., per cents, or excellents, goods, fairs, etc., mean certain 
points on the scale, her ratings will have a definite meaning to 
the pupil, can have the same meanings that similar ratings by 
other teachers in the school have, and may be used to measure 
the actual improvement of the pupil month by month and year 
by year. She can more easily and more accurately measure the 
relative values of the different methods of teaching which she 
may from time to time employ, of different lengths of periods 
for drill, and the like. 

A principal or supervisor or superintendent of schools needs 
to measure the quality of the handwriting of individuals, of 
classes, and of all classes of the same grade, in a school or 
system. If he has such measures honestly made by the scale, he 
can compare the work of one teacher with that of another, the 
work within his own school or city with that of other schools or 
cities and with that of his own city five years later, the work of 
schools using one system of writing with that of schools using 
other systems, and the like. If he tried without the scale to esti- 
mate the superiority or inferiority in handwriting of twelve-year- 
olds in city A to twelve-year-olds in city B, he would have to 
collect many samples in both cities and have them graded alike. 
He could define the amount of difference found only by actually 
exhibiting it in samples or by making out a scale like ours, defin- 
ing it as I have done, and expressing the difference as such a 
distance on the scale. With the scale in use in both cities, on the 



1 8 Handwriting 

contrary, if marks are honestly given by the teachers, the 
superiority or inferiority of any group will be measured by the 
difference in the scale-values of the marks themselves. 

The scientific student of education will use the scale to mea- 
sure the quality of samples of handwriting from individuals, 
classes, cities, groups chosen for grade, age, sex, method of 
teaching, or length of time devoted to writing, and from any 
other sources. He will also be able to use any marks or ratings 
honestly given by teachers or others. 

Whoever has any occasion to define a standard of quality in 
handwriting can define it unmistakably and conveniently by the 
scale. Business men can decide what quality they wish the 
schools to secure in the boy fourteen years old who is to apply 
for clerical positions. A supervisor can inform all the teachers 
of, say, grade 7 that the minimum requirement is, say, quality 
11, at a rate of 50 letters per minute, that the average pupil 
must be made to write at quality 13 at a rate of 60 letters per 
minute, and so on. Whatever standard is set will be absolutely 
defined by those who set it and will be clear to all those who are 
to follow it. 

The pupil himself may profitably know and use the scale. He 
may see by it what is expected of him and may tell how nearly 
he reaches the standard and how much he has gained. 

Even if precision is not desired in the estimate of the quality 
of handwriting, — even if good and bad or satisfactory and un- 
satisfactory are the only ratings to be given, — the scale is none 
the less useful. For if good and bad, or satisfactory and unsatis- 
factory are to mean anything, they must mean handwritings 
above and below some point on some scale of merit. They can 
be properly defined only by locating that point. And until some 
better scale is available that point can be located only by ex- 
hibiting samples or by stating the numerical value these samples 
would have on our scale. 

To put the whole matter in a word, any measurement of the 
quality of handwriting should be made by the scale and reported 
in terms of the scale, for substantially the same reasons that any 
measurement of the length of an object should be made with a 
linear scale and reported in meters or feet. 



The Measurement of the Quality of Handwriting 19 

Measurements may be made by the scale without the com- 
parison of the sample with the actual scale itself. Just as one 
uses his experience of feet and inches as a mental standard 
whereby he estimates more or less accurately the length of 
pencils, tables, windows, and the like, without an actual ruler or 
tape, so one may come to estimate that this sample of writing is 
about quality 16, that one about quality 9, and the like, from the 
mental standard left from examination and use of the actual 
scale. The scale should always be present for reference in any 
measurement which requires exactitude, but it will do its greatest 
amount of service, not by actually serving as a foot-rule for 
quality in handwriting, but by creating in the minds of teach- 
ers mental standards to be used in even the most casual ratings 
of everyday school-room life. To one who uses the scale quality 
18 or quality 15 or quality 7 comes to be a definite agent in de- 
termining all judgments, just as 18 inches or 15 pounds or 7 
dollars is. Just as a child learns to think about length correctly 
and with fair precision without a ruler in his hand, by having 
measured off lengths with it, so teachers may come to think about 
handwriting correctly and with fair precision without the scale 
before their eyes by having measured handwritings with it. Just 
as the thermometer teaches us to supplant the vague " very 
cold," " cold/' " moderate," " warm," " hot," and " very hot " 
by " about o," " about freezing," " about 60 degrees," " about 70 
degrees," " about 80 degrees," " nearly 100," and the like, so the 
graphometer can teach us to supplant the vague " illegible," 
" very hard to read," " a good plain hand," and the like, by judg- 
ments which mean something definite and constant to those who 
make and those who hear them. 

Section 6. A Scale for Quality in Adult Women's Hand- 
writing 

The scale for adult women's handwriting consists of only six 
points, each represented by only one sample. Let us call these 
samples a, b, c, d, e, and /. They represent the best selection 
that I could make of writings ranging from nearly the best to 
nearly the worst of the ordinary writings of some five hundred 
women teachers and students and differing progressively by 



20 Handwriting 

equal degrees of merit. The derivation of the scale was as 
follows : 

Thirty judges rated samples a, b, c, d, e, and /, together with 
from 37 to 456 other samples. The ratings given were from 
1 (the lowest grade) to n (the highest), grades 1 to n being 
roughly shown by samples and the requirements being made that 
the grades 2, 3, 4, 5, etc., should represent grades of merit dif- 
fering by equal steps. The number of the samples was reduced 
from 456 to 37 by gradually dropping samples which seemed 
unlikely to be near the points 1 to 1 1. The result of the thirty 
ratings is shown in Table II. 

Table II 

The Quality of Samples a, b, c, etc., as Measured by 30 Judges 
from the Original Writings 

Quality Frequencies of Each Quality for Each Sample 

a b » c d e f 

1 20 I I 

2 7 12 

3 I 6 2 I 

4 267I 

5 2 10 6 I 

6 1532 

7 3862 

8 1 1 3 4 

9 1563 

10 166 

11 3 5 19 

Bearing in mind that a rating of quality 1 means 1 or worse 
than 1 and that a rating of quality 11 means 11 or better than 
11, it is clear that in the combined judgment of all 30 judges 
a, b, c, d, e, and / represent qualities progressing by approxi- 
mately equal steps. Thus 10 of the judges ranked a as better 
than 1, 10 ranked b as better than 3, and 10 ranked c as better 
than 5, 12 ranked d as better than 7, and 11 ranked e as better 
than 9. Of the 20 judgments of a as 1, it is probable that about 
10 would have been " worse than 1 " had the series included a 
lower range. Of the 18 judgments of /as 11, it is probable that 
about 10 would have been "better than 11 " had the series in- 
cluded a higher range. The median values of a, b, c, etc., with 
this interpretation of the grades 1 and 11, are: 1.0, 2.833, 5-°> 



The Measurement of the Quality of Handwriting 21 

7.125, 8.833 an d 10.94, tne differences in quality being respec- 
tively 1.833, 2-167, 2.125, 1.708, and 2.107. 

These six samples were then printed and were graded in their 
printed form, together with seven other samples of approxi- 
mately the qualities 1, 3, 5, 5, 7, 9 and n, by thirty-eight judges. 
The ratings in this case were in 6 grades, to progress by equal 
steps. These were called by the judges 1, 2, 3, 4, 5 and 6, but 
represent respectively 1, 3, 5, 7, 9 and 11 of the gradings just 
presented in Table II. Hence in Table III, which gives the re- 
sults of the gradings by these thirty-eight judges, I shall use 1, 3, 
5, etc., for 1, 2, 3, etc. 

Table III 

The Qualities of Samples a, b, c, etc., as Measured by 38 Judges 
from the Printed Reproductions 

Quality Frequencies of Each Quality for Each Sample 

a b* c d e f 

1 32 7 

3 5 21 8 3 

5 1 9 19 12 1 

7 9 19 6 3 

9 2 3 22 13 

11 1 9 22 
* Only 2>7 judges rated this sample. 

The median ratings for a, b, c, etc., are .8, 3.1, 5.1, 6.4, 9.1, 
10.7. 

These thirteen printed samples were then rated together with 
from 58 to 104 samples of children's handwriting, including 
samples much better than the best of the adults', by 26 judges. 
The ratings were from 1 to 11, but the meanings of these num- 
bers were unlike those attached to them in Tables II and III, 
except in the case of the 1. The 3, 5, 7, 9, and 11 of Tables 
II and III have approximately the values 2.4, 3.8, 5.2, 6.6, and 8. 
Finally, the thirteen samples were rated, together with 120 sam- 
ples of children's writings, including some still better and some 
still worse, by 9 judges. The ratings were o to 12 but the 
values of the 1, 3, 5, 7, 9, and 11 of Tables II and III were, as 
before, approximately 1, 2.4, 3.8, 5.2, 6.6 and 8. The median 
values attached by the 35 judges were, for a, b, c, d, e, and /, 
in order, 1, 2.4, 3.83, 5.3, 6.5, and 7.9. 

We have then as a result of the three series of judgments, 
numbering 103 in all, the following: 



22 Handwriting 

Differences between a and b, b and c, c and d, etc. : 

I. Using the median ratings of 30 judges (ink samples) : 1.83, 
2.17, 2.13, 1.71, 2.11. 

II. Using the median ratings of 38 judges (print) : 2.3, 2.0, 
1.3, 2^, 1.6. 

III. Using the median ratings of 35 judges (print, long 
series) reduced to equivalences with (I) and (II) : 2.0, 2.04, 
2.1, 1.7, 2.0. 

Average differences: a-b, 2.04; b-c, 2.07; c-d, 1.84; d-e, 2.04; 
e-f, 1.9 1. 

The approximate equality of the steps may be verified by as- 
certaining how often b is rated higher than a, how often c is 
rated higher than b, etc., that is, by an adaptation of the so-called 
method of right and wrong cases. The facts are as follows : 



Comparisons of a, b 



Table IV 








b, c, d, e, AND f BY 


102 Judges 




Long series, 
written 
samples 


Series of i 
printed 
samples 


3 Series of 71 
to 133 printed 
samples 


All 
series 
together 


30 


37 


35 


102 


25* 

26* 

23 

23 
23 * 


26 

25* 

25* 

29 

24 


23 

27* 
25* 

19 
26 


74 
78 
73 
7i 
73 



No. of comparisons 

b rated as better than a 
c rated as better than b 
d rated as better than c 
e rated as better than d 
f rated as better than e 

In the starred cases the obtained figure was 1 less than that 
printed, but the number of comparisons it was from was also 1 
less than that printed at the top of the column. 

Samples a, b, c, d, e, and / thus represent points on a scale 
of quality differing each from the next by approximately equal 
steps. We can properly call their values in order x, x + 2, x + 4, 
x + 6, x-\-S, and #+10 where 1.0 equals a difference roughly 
equal to one-tenth of the difference between the best ten and the 
worst ten of a thousand samples each from an adult woman 
student and x equals the average quality of the worst ten of the 
thousand. To be more precise we should call them, in order, x, 
x + 2.0, x + 4.1, x + 6.0, x -V 8.0, and x + 9.9. 



The Measurement of the Quality of Handwriting 23 

To turn these values into numbers referring to zero merit as a 
starting point we must define zero merit for adult handwriting 
and measure the distance of x from it. 

This I have not attempted to do at all adequately since the 
need of an elaborate scale is not nearly so great in the case of 
adult handwriting as in the case of children's writing. Quality 
x of the adult scale is judged by the average of some forty indi- 
viduals to be approximately equal to quality 8 of the children's 
scale. A difference of 1.0 along the adult scale is judged to be 
approximately equal to a difference of .7 along the children's 
scale. If we take the zero point for adults as approximately the 
same as for children of grades 5, 6, 7, and 8, the qualities of 
a, b, c, etc., may be taken as approximately equal, in order, to 
8, 9.4, 10.8, 12.3, 13.6, and 14.9 or 15 on an absolute scale whose 
zero is a writing recognizable as an attempt to write, but of zero 
merit. Such a numbering would not be far wrong. 

This adult scale very much needs samples of other styles at 
each point. Perhaps I should have delayed printing it until such 
had been obtained, but the labor and expense of collecting and 
selecting, by grading and gradual elimination, samples to fit ex- 
actly certain places on the scale is very great. The present scale 
has required thousands of gradings. It will be of great value in 
economizing the time and money of any one who wishes to make 
a better scale, if in no other way. 

As a matter of fact, in spite of its lack of samples of all 
styles at each point, it will also be of service in every case where 
the quality of a woman's handwriting is to be definitely known. 

For example, (1) the authorities of a college or a normal 
school wish to set a clear standard as to how good handwriting 
must be in order to make an examination paper, or a composi- 
tion, or other written work, acceptable. If they set this standard 
as " at least as good as quality c of the Thorndike scale " every 
student, every member of the teaching staff, the faculties of other 
colleges, and the public can tell just what the standard is. There 
can be real as well as " paper " uniformity in the standard. 

(2) In civil service examinations, examinations for teacher's 
licenses and the like, the standard of a certain quality by the 
scale at a certain minimum speed can be set and the candidates 



24 Handwriting 

can be exactly, impartially, and uniformly (all over the country, 
if desired) rated. 

(3) The relation between (a) ability in handwriting under the 
pressure of school drill to (b) ability in handwriting in later life 
requires for study some adult scale. So also with any other 
relation of the quality of adult handwriting to anything. 

I shall be indebted to any one who will send me samples of 
adult women's handwriting, especially of vertical writing of 
qualities d, c, b, a, and worse, of pronounced slant writing of 
qualities d, e, f, and better, and of pronounced backhand writing 
of all qualities. Each such sample should be accompanied by a 
statements of all the grades assigned to it on our scale by ten or 
twelve competent observers, each of whom judges in entire 
ignorance of the judgments made by all the others. It is de- 
sirable, though not necessary, that the writings be on unruled 
paper. 

Section 7. The Derivation of the Scales 1 

Certain partial descriptions of the means and methods by 
which the children's scale and adult women's scale were derived 
have been given in sections 2 and 6. A full account of the deri- 
vation of either is inadvisable both because it would necessarily 
be extremely long and because much of the work done was such 
as I now know, from the very experience of doing it and seeing 
its results, to have been unnecessary. 

I shall therefore give only such notes as are likely to be helpful 
to any one who is stimulated by this scale to construct similar 
scales for other educational products. 

To construct a scale by which to measure various qualities 
(that is, amounts of merit) in handwriting ranging from, say, x 
to x -f y, it is desirable to have samples of qualities, not only of 
every degree from x to x + y, but also of qualities worse than jf 
and of qualities better than x + y. The reason is that otherwise 
the exact values of samples at x or x plus a slight amount and of 
samples at x + y or x + y minus a slight amount cannot be di- 
rectly measured, but only inferred. 



1 The reader uninterested in educational measurements is advised 
to skip this section, and to turn at once to the more immediately 
practical discussion of differences amongst school systems with respect 
to speed and quality of handwriting. 



§1 



3 i 4 



X 



Hi 

i-tiT 



j< ; 



U' 



£ cS 



y 






it 



HI' H 

* | 5 4 J * 







1 t* 



^-M - 
i hit 1=5= 



i f|H 








The Measurement of the Quality of Handwriting 25 

For example, call x 1 and y 10. X + y then being n, x or 1 is 
nearly the worst and x + y or 11 is nearly the best of a series of 
samples, ranging continuously from x to x -\- y. 

If now any one is required to fix in mind 11 points including 
x (or 1) and x + y (or 11) differing each from the next by 

equal amounts, and to rate each of the samples as 1, 2, 3, 9, 

10, or 11, according to which of these mentally fixed points it 
seems most like, he can err by rating a sample as 2 or 3 when 
it is really 1, but cannot err by rating it o or minus 1 when it is 
really I. Similarly he can err by rating it 9 or 10 when it is 
really 11, but cannot err by rating it 12 or 13. For a sample 
really close to point 11, rated in the way just described by 33 
judges, the results were: 

Rated as 11 by 21 judges 
Rated as 12 by 7 judges 
Rated as 9 by 3 judges 
Rated as 8 by 1 judge 
Rated as 7 by 1 judge 

The apparent average rating would then be 10.4 and the apparent 
median rating 10.7. When, however, the samples are increased 
by some of the real quality x + y+i (or 12) and the ratings 
are to be made at twelve points including x-\-y+i (or 12), a 
certain proportion of the judges rank the sample in question 12 
and the average and median are raised to nearly 11. 

Unless the set of samples to be rated includes some samples 
one, two, three, and even four grades better than the best quality 
(x + y) to be represented in the final scale and also some sam- 
ples one, two, and three grades worse than the worst quality (x) 
to be represented in the final scale, one cannot get the values of 
x + y and x themselves save by inference. 

Hence, to make a scale for the handwritings of, say, 10-year- 
old school children conveniently, it is necessary to have a collec- 
tion of samples varying in quality from much below the worst to 
much above the best of their writings. This involves the use of 
" unnatural " samples, which may seem very objectionable, but 
which as a matter of fact does little or no harm. 

In the case of a scale for the merit of English compositions 
by high-school pupils one should start from a collection of com- 



26 Handwriting 

positions ranging by small gradations from compositions much 
worse than the worse point on the final scale is to be, to composi- 
tions much better than the best point on the final scale is to be. 
Here the extremely bad ones may be obtained by artificial con- 
struction, from the feeble-minded, or from very old and stupid 
grammar-school children. The extremely good ones may be 
obtained from the printed or manuscript compositions in youth 
by gifted authors. 

To get samples exactly situated at points differing progres- 
sively by equal steps requires that the original set range from 
one extreme to the other by very slight gradations. This means 
for practical purposes that one must have at the start a very 
large number of samples. After these have been graded by 
enough judges to rate each roughly, only those which are near 
the points to be represented by the scale need be graded further. 
As the value of each sample of this narrower selection is deter- 
mined more exactly by further judgments, only those very near 
the points to be represented on the final scale need be preserved 
for still further judgments ; and so on till the values of enough 
samples are determined to the degree of precision required for 
the scale itself. 

Points on the scale exactly determined, but not at progres- 
sively equal steps, can be got with far less labor. If, for example, 
after a single rating I had picked samples at intervals from the 
best to the worst and then had only these few samples rated by 
the twenty to seventy judges, the value of each could have been 
stated nearly as exactly as is the case in the samples of the scale. 
But they would form a series like 17.33, x 6.65, 16.28, 15.82, 15.40, 
15.47, 15.23, 14.95, J 4-7> etc -> instead of the approximate 17, 16, 
15. 15. I 5, 15, 15, I4» I3» 13, 13, etc., of the scale. They would 
have served the purpose of a scale as well so far as aiding an 
observer to make exact measurements which any other observer 
could verify, and to report them unambiguously, but the labor of 
allowing for the decimal values or of computing measures ex- 
pressed in awkwardly long numbers would burden each person 
using the scale. If the scale were designed for use only by scien- 
tific investigators of education, I should have economized in re- 
spect to the number of samples rated, had far more ratings of 
each sample, and presented a scale of very exactly determined 



The Measurement of the Quality of Handwriting 27 

qualities but at irregular intervals. For the common use of 
pupils, teachers, and supervisory officers a less precise scale by 
approximately equal steps seemed far more valuable. Also the 
precise evaluation of each sample can be determined by many 
students each spending independently a little effort in getting 
the samples which I print rated ; whereas the selection of samples 
varying by equal steps can be managed best under one indi- 
vidual's supervision. 

It is possible that the determination of the amount of dif- 
ference between two samples by the percentage of judges notic- 
ing the difference is preferable to the determination by the 
amount of difference between their median values as given by 
judges attempting to apply to each a scale of mentally equal dif- 
ferences. I used both methods. Experience of their use provides 
many facts of importance to methods of quantitative work in 
both psychology and education, but the facts would be of interest 
to only the small proportion of readers to whom surfaces of fre- 
quency of errors in judgment are familiar and esteemed friends. 

In general, the experience in constructing this scale gives great 
encouragement to the hope that for many educational facts, units 
and scales may be invented that shall enable us to think quanti- 
tatively in somewhat the same way that we can about facts of 
physics, chemistry, or economics. It has been commonly sup- 
posed that the great complexity of such facts as examination 
papers in spelling, manifestations of interest in history, acts of 
moral significance, habits of industry, essays, poems, inventions, 
replies to questions demanding logical inferences, and other like 
results of education, prevents the samples composing any one 
such group from being measured by any one linear scale at all 
comparable to a foot rule or thermometer or galvanometer. 

It is true that some judges find it hard to judge handwriting 
for the complex of legibility, beauty, ease, " character," etc., into 
which " quality " or " goodness " or " merit " resolves itself. But 
none of them found it impossible to do so, and most of them 
rated the writing for the complex, — " merit or goodness in your 
opinion," — as readily as an appraiser would rank articles of sale 
by money price, or as a little child would arrange pieces of paper 
in the order of their size regardless of the fact that some were 
squares, some circles and some triangles. 



28 Handwriting 

The entire history of the judgments of the merit of handwrit- 
ings supports the claim that if a number of facts are known to 
vary in the amount of any thing which can be thought of, they 
can be measured in respect to it. Otherwise, I may add, we 
would not know that they varied in it. Wherever we now 
properly use any comparative, we can by ingenuity learn to use 
defined points on a scale. 



PART II 

The Speed and Quality of Handwriting in Seven 
School Systems 

The conclusions to be reported in sections 8 to 13 are based 
upon about 3000 samples of handwriting made in a formal test 
conducted by Dr. C. W. Stone 1 in seven school systems, five 
public and two private. These samples were scored in about 700 
cases by six judges using no scale, and in the remaining cases 
by two judges using an early form of the scale. The two judges 
differed by more than one step of the scale in only three samples 
out of ten. Thus the combined opinion of the two judges, 
though giving only a rough estimate for any single sample, is 
sufficiently precise for estimating the average quality of the writ- 
ing of a group of thirty or more pupils, such as a school class. 

Section 8. Differences between Systems 

It is known that school systems differ greatly one from another 
in arithmetic (Stone, '07) and much less in spelling (Rice, '97, 
Cornman, '02). They differ markedly in handwriting if we 
compare them for its quality, but six of the seven differ hardly 
any when they are compared for quality of writing done at the 
same speed. 

Thus in the case of the eighth grade the median quality (for 
the whole grade) of writing done " as well as you can " varies 
from 1 1.4 of the Thorndike scale in system A to 14.5 in system 
F (see Table V) ; the median quality for the whole grade of 
writing done " at your usual rate " varies from 10.3 in system A 
to 14.0 in system G (see Table V). 

In average speed of the eighth-grade writings, there is a range 
from system G with 37 letters a minute to system B with 67 



1 To whom I am greatly indebted for permission to use this material. 
The ratings by the six judges were also obtained by him. 

29 



30 Handwriting 

letters per minute in the careful writing, and, in the writing at 
one's usual rate, a range from system G with 50 letters per 
minute to system C with 80. (See Table V.) 

Table V 

Speed Irrespective of Quality and Quality Irrespective of Speed in 
the Case of the Handwriting of Seven School Systems. Median 
Results for Eighth-Grade Pupils (Upper Figure) and Seventh- 
Grade Pupils (Lower Figure). 



School system 
Letters per minute in 
careful writing 


A 
61 
46 


B 
67 

48 


C 
66 
62 


D 

51 
46 


E 
48 
43 


F 

47 
48 


G 

37 
26 


Letters per minute in 
" natural " writing 


79 
68 


75 
63 


80 

75 


60 
61 


63 
56 


63 
64 


50 
36 


Quality (by T. scale) 
in careful writing 


11. 4 
11. 4 


11. 8 
11. 7 


11. 7 
11. 4 


12.0 
11. 7 


12.3 
13.0 


14.5 
14.0 


14. 1 
13. 1 


Quality (by T. scale) 
in natural writing 


10.3 
10.3 


11. 2 
11. 1 


11. 
10.6 


11. 7 
11. 3 


11. 6 
12.7 


13.7 
13-0 


14.0 
13.0 



If we compare the eighth-grade pupils of the different schools 

who wrote at roughly the same rates, they range as shown in 

Table VI. 

Table VI 

Quality of Handwriting at Roughly the Same Rate in Seven School 

Systems 

Median Results for Eighth-Grade Pupils 
System A B C D E F G 



At 20-29 words in 4 

minutes 14.5 13.0 15 

At 30-39 words 11. 5 11. 3 11. 6 12.3 12.3 14 

At 40-49 words 11. 5 12.0 12.0 11. 8 12.3 14 

At 50-59 words 11. 5 11. 6 11. 1 11. 1 11. 6 13 

At 60-69 words 10.3 11. 8 11. 5 11. 3 11. 6 13 

At 70-79 words 10. o 10.8 1 1. 3 



4 14.8 

5 14.2 
4 15.3 
o 11. 7 

6 



Median Results for Seventh-Grade Pupils 

System A B C D E F G 

At 10-19 words 13.3 14-5 13-5 

At 20-29 words 12.3 13.3 13.0 13.6 14.2 13.0 

At 30-39 words 11. o 11. 8 12.3 13.3 14.2 13.0 

At 40-49 words 11. 11. 8 11. 3 11. 7 11. o 13.3 11. 8 

At 50-59 words 10.3 11. 4 11. 1 11. o 11. 8 13.0 

At 60-69 words 10. o 11. 3 10.5 10. o 11. 4 11. 8 

At 70-79 words 9.8 9.8 9.9 

That these likenesses and differences between systems are not 
due to chance but are true characteristics of the school systems, 
is proved by the fact that the measurements come from so many 
cases as to be subject to only very slight chance or accidental 



The Speed and Quality of Handwriting 31 

errors, and also by the slight differences found between buildings 
or classes within one system. For instance, of three schools 
of system F, the seventh grades of the two most unlike differ in 
quality at the same rate by only three tenths of a step, the best 
one being about 3 per cent better than the worst. Of three 
schools of system G, the seventh grades of the two most unlike 
differ in quality at the same rate by only four tenths of a step, 
or 4 per cent. The average difference of one school from another 
within the same system is little if any over two tenths of a step 
or 2 per cent. 

The comparison of systems by the quality of the handwriting 
at the same rates is not, however, perfectly just. For in so 
doing we are comparing the more rapid writers of some systems 
(especially G) with the slower writers of other systems (especi- 
ally A, B, and C). Now in general the more rapid writers of 
a system would write a little better at the average rate for that 
system than would the slower writers of the same system. If, 
for instance, all the seventh-grade pupils of any systems were 
made to write at different speeds until for each one a record at 
the rate of 64 letters per second was secured, we should find 
that the pupils whose undirected rates were higher than 64 
would at the 64 rate do better than those whose undirected rates 
were below 64. 

Also, within the 10-19 or 20-29 or 30-39 word group, there are 
prejudicial differences between the schools. In grade 8 of school 
G, for example, the 20-29 word group will contain a larger per- 
centage of pupils writing at rate 20-25 than it will in grade 8 of 
school F. In comparing a slow-writing school with a fast- 
writing school, by the quality of groups roughly equal in speed, 
we thus give an unfair advantage to the slower writing school. 

To make the comparison just we would have to find equiva- 
lents in quality for each degree of superiority in speed, so as to 
be able to combine the two into a score for general efficiency in 
handwriting for each individual. Such an investigation of the 
exact relative values of certain increases in speed and in quality 
should some time be made. I have not had time or means 
to make it as yet. As our data are, in the case of the 8th grade 
pupils, systems A, B, and C can be compared inter se for they 
are substantially alike in speed. So also can systems D, F, and 



32 Handwriting 

F. A, B, and C can be compared with D, E, and F with only- 
slight chance of error by taking the " careful " work of A, B, 
and C and the " natural" work of D, E, and F. But the selection 
of cases at equal rates slightly favors D, E, and F at the expense 
of A, B, and C and favors G at the expense of all the other six 
systems. 

Of systems A, B, and C in the eighth-grade writing, A is the 
worst by about 5 per cent. Of systems D, E, and F, F is the 
best by about 25 per cent, D and E being alike. F is equal to 
G in quality and nearly 30 per cent superior in speed. Roughly 
estimating the equivalence of A's greater speed and F's superior 
quality, F seems to be about 30 per cent better than A. A, B, 
C, D, and E are of about equal merit. The data to support these 
comparisons were given in Tables V and VI. 

The records from the seventh-grade pupils give substantially 
the same result as those from the eighth-grade pupils just stated. 
A, B, C, D, and E differ little, A being about nine tenths as 
good as the others. F is about 25 per cent better than B, C, 
and D. E is a little better than B, C, and D. F shows writing 
as good as G's at a speed nearly six sevenths greater. These 
facts are derived from the data of Table VI, an allowance being 
made for the two constant sources of injustice in such data, and 
from the data of Table V, G seems, speed and quality both being 
taken into account, to be little or no better than B, C, D, and E. 

Section p. The Relation of Differences in Results to Differ- 
ences in Means and Methods of Teaching Handwriting 

Not much can be proved by relating these differences to dif- 
ferences in means and methods of teaching handwriting, since 
the number of school systems studied is so few. F, which is so 
markedly superior, uses vertical writing of a special system 
arranged by the supervisor of handwriting, uses writing books, 
devotes 75 minutes weekly to specific instruction and practice in 
writing in grades 5, 6, and 7 (of what is done up to grade 5, 
I have no report), and 30 minutes weekly in grade 8. The 
teachers in general follow the same system in writing on the 
blackboard. 

The other systems are about alike in general merit in hand- 
writing, A, B, and C gaining speed at a reasonable cost in 



The Speed and Quality of Handwriting 33 

quality. A and B teach no fixed system, devote no time to pen- 
manship as such, and permit the teachers to write according to 
any or no system. C uses a medium slant or intermediate or 
business system, uses copy books, devotes 50 to 60 minutes 
weekly to penmanship as such, and has the teachers use the 
system taught to the pupils. D uses a modified Spencerian with 
copy books, devotes 50 to 75 minutes weekly in grades 5 and 6, 
and 75 to 100 in grades 7 and 8, to penmanship as such, and has 
the teachers follow the system in their own writing. E uses a 
forward slant, and devotes 100 minutes in grade 6, 60 to 90 in 
grade 7, and 60 in grade 8, to penmanship as such. 

System G uses an intermedial writing, devoting from 60 to 
90 minutes weekly to special instruction and practice in grades 
7 and 8. The teachers use the same system in their own writing 
on the blackboard. 

What these facts do prove is : First, that at least three systems 
(C, D, and E) get little or no better results at a time cost of 
about 75 minutes a week than two systems (A and B) do at 
zero time-cost; second, that one system (F) at no greater time- 
cost than C, D, and E gets results about 25 per cent better than 
they do; and third, that practice for quality may secure it only 
at the cost of speed. The teachers in A and B are better paid 
than those in the other cities, so that the success of these schools 
at no time-cost might not be generally attainable. 

Leaving F out of account, the differences of these school sys- 
tems in the method of teaching handwriting, in the time devoted 
to it, and in the ideals of the system in respect to it are of incon- 
siderable influence upon efficiency. One makes its pupils write 
very well at very slow rates, the others vary a little in quality 
with small inverse variations in speed. On the whole, in spite of 
the achievement of system F, efficiency in handwriting seems, 
like spelling, and unlike arithmetic, to be under present condi- 
tions not very much influenced by the management of the schools. 

Section 10. Differences between Individuals within the Same 
School System 

We have seen that the school systems, with the exception of 
F, differ little among themselves in the efficiency of the hand- 
writing which they secure. Individual pupils on the contrary 



34 Handwriting 

do differ greatly. Excluding system F, we still find amongst 
eighth-grade pupils a range from a pupil writing only 55 letters 
per minute, at quality 7.5 up to a pupil writing 79 letters per 
minute at quality 15.2. Of the 15 eighth-grade pupils writing 
at the same rate (53 words in 4 minutes) the scores for quality 
(excluding system F) run from 9.1 to 14.6. 

The variation among pupils of the same grade in the rate of 
writing of the same quality is also large. In the seventh grade 
of system F, for instance, of the writings of the pupil's usual 
rate there were 74 samples of from quality 12.7 to 13.3. The 
number of words written in four minutes ranged from 19 to 87. 
The 87 may possibly be due to overtime writing. The next 
highest case was yy, and the next 70. After the two cases at 19 

Table VII 

Relative Frequencies of Different Speeds of Writing at Natural 
Rate, the Same Quality of Writing Being Secured 

Number Frequencies 

of words F, 7th grade G, 7th grade 

IS 2 

17 

19 2 

21 2 

3 I 

5 2 2 

7 12 

9 4 2 

31 2 2 

3 4 

5 3 

7 5 

9 3 1 

41 3 

3 5 

5 5 

7 2 

9 4 1 

5i o 

3 4 

5 5 

7 6 

<? 5 

61 3 

3 3 

5 o 

7 1 

9 1 

Also 1 case at 77 and 1 at 87. 



The Speed and Quality of Handwriting 35 

there is a gap till 25. From 25 to 70 there is a fairly continuous 
distribution. Allowing for the time of reading the copy and 
other disturbing factors, it still appears certain that within the 
same grade some pupils spend at least three times as long in 
writing the same amount at the same quality. The facts in de- 
tail appear in Table VII. 

Individual pupils within the same grade then show a range 
of difference much greater than that between the fifth grade of 
the worst system and the eighth grade of the best. 

Section 11. The Relation amongst Individuals between Speed 
and Quality 

Rapidity is in and of itself a good sign. If we know nothing 
about one score or so of pupils save that they are rapid writers 
and nothing about another score save that they are slow writers, 
we can prophesy that at the same rate the former group will on 
the average do writing of a higher quality. 

Thus there were 20 seventh-grade pupils in system F who, 
in writing naturally, varied from 29 to 64 words in four minutes, 
but who wrote just the same number of words (33) in the test 
in careful writing. The naturally slower ten showed at the rate 
of 33 a median quality of 14.5, the more rapid ten a quality of 
14.8. This occurred in spite of the fact that for the slower ten 
writing at a rate of 33 was more like their usual habits. It is 
to be expected that, if all had been made to write at, say, 73 
words in four minutes, the difference would have been greater. 
Dividing three similar sets each into a slower and a faster half 
we find for the naturally slower half a median quality of 13.9 
and for the faster half a quality of 14.2 when both wrote at an 
identical rate. 

Of course the same pupil will not write as well at a rapid as 
at a moderate rate, and if we mix pupils from a school in which 
rapidity is gained at the cost of quality with pupils from a 
school in which quality is gained at the cost of speed the rapid 
writers will seem to be the poor writers. But, in and of itself, 
rapidity is a sign of ability which if directed toward quality could 
secure high results in that instead. 



36 Handwriting 

Section 12. The Relation of the Quality of Slow Writing 
to the Quality of the Rapid Writing by the Same individual 

Amongst school children there is a close relation between the 
quality of writing at a natural rate and that at a slower rate. 
For instance, let us take the 26 children in grades 6 and 7 of one 
school of system F, who write at a rate of 33-37 inclusive in the 
first test and at a rate of 52-60 inclusive in the second test and 
ask whether high rank for quality of writing at a slow rate in- 
volves high rank for quality of writing at a speed some 60 per 
cent greater. It does, the average correlation for three groups 
like the one described being about .6. Part of this correlation is 
due to the differences of the individuals in maturity, but this 
spurious correlation is offset by the attenuation due to the chance 
variations in the measures related. Of course, the same relation 
is not thereby proved to hold also between quality of writing at 
one's natural rate and quality of writing at a rate much slower 
than it. But I believe that it would, and that, although writing 
at one rate is not identical with writing at a different rate, writ- 
ing is, over a wide range of rates, so similar a function that train- 
ing which improves its quality at any one rate may be expected 
to be of benefit at many others. This does not of course make it 
any less desirable to practice handwriting at the rate at which 
one will have to write, but it does make the custom of slow, 
elaborate writing less pernicious than it might be were the habits 
at different rates almost or quite independent of one another. 

Section 13. Miscellaneous Comments 

The Effect of Reduction from a Pupil's Natural Rate upon the 
Quality of his Handwriting 

The gain in quality which a pupil secures by writing more 
slowly than his natural rate is not great. Sixty-one pupils, whose 
natural rate was from 52 to 58 words in four minutes, by reduc- 
ing their speed to 32 to 36 words in four minutes, that is, by 
writing only two thirds as fast, gained on the average in quality 
less than one step of the scale. The loss in quality which a pupil 
suffers by writing more rapidly than his natural rate has not 
been measured. 



The Speed and Quality of Handwriting 37 

The Significance of the Inferiority of Adults' Handwriting 

That children in the last two grammar grades can write so 
much better than adult women-teachers do customarily write is 
an important fact. Considering it in connection with the fact 
that above quality 11 there is very little difference in legibility, 
one is tempted to advocate the heresy that children are taught 
to write too well. I personally do advocate it. If school boards 
would furnish, for the use of children electing " writing " as a 
study in the last two grammar grades, typewriting machines, I 
should certainly advise the transfer to typewriting of a child in 
these grades whose writing at 60 letters a minute consistently 
reaches quality 13. For, the amount of practice required to ad- 
vance such a pupil to quality 16 at a rate of 75 letters a minute 
would much more than suffice to advance him to substantially 
errorless machine writing at that rate. The value now attached 
to the high qualities of handwriting is, of course, largely ficti- 
tious. Employers who can afford such high qualities of writing, 
buy machines to produce them. For writing cash checks, simple 
book-entries, labels, and the like, a good plain hand or our 
quality 12 is entirely adequate. For attaining the higher qualities 
(15-18) the machine is a more economical tool than the pen, 
and in my opinion should be provided by those schools which re- 
quire such qualities. Further, such qualities should, in my opin- 
ion, be required of children in the elementary schools, only when 
they have elected writing as a vocational subject. For the data 
from the adult women-teachers make it practically certain that 
the ability to write above quality 14 will not be exercised in life 
except as a part of a clerical trade. If very, very few teachers 
find it worth while to maintain qualities above 14, it can hardly 
be supposed that it will be worth while for mechanics, house- 
keepers, farmers, and dressmakers to do so. 

It seems likely also that handwriting has been, and is, a case 
of a common practical fallacy, which may be called " learning for 
learning's sake." When certain facts or acts of skill are teach- 
able, teachers tend to teach them regardless of any intelligible 
service performed by them other than the doubtful one of " dis- 
ciplining " the mind or hand or eye. Since, for instance, arith- 
metical methods of extracting cube root have been learned by 



38 Handwriting 

teachers and can be taught to children, we teach them, regardless 
of the fact that no person in his senses would extract a cube 
root in that manner. Similarly it is doubtful if any intelligent 
person would (except to become a teacher of handwriting!) pay 
the necessary time-cost to acquire the ability to write at 75 letters 
or over per minute at quality 17 or better. He would, of course, 
learn to typewrite instead. And if an intelligent person has been 
artificially induced to get that ability in school, he promptly loses 
it thereafter. 

The Relation between an Individual's Ability in Handwriting 
and his General Intellectual Ability 

I have measured the correlation between scholarship and 
quality of handwriting in the case of adult women students in 
Teachers College. These students comprise in the main teachers 
of from 1 to 15 years of experience who have left their work 
temporarily for further academic and professional training. The 
academic marks represent intellect more often than college marks 
in general do, because what intellect a student has is more likely 
J to be devoted to scholarship in a professional school than in a 
^college. But, on the other hand, achievement in professional 
courses for teachers is probably aided by experience in teaching. 
Finally, the standards of marking vary with instructors, and 
probably somewhat with departments, so that two students, each 
taking the bulk of her work in some one department, may for 
equal scholarship receive different average grades. 

The marks for quality of handwriting on the other hand are 
very exact. For each student I have from one to three judg- 
ments in each of ten samples taken at random from her writing, 
— in all a total for each student of nineteen judgments. The 
marks for handwriting have in fact probable average deviations 
of the true from the obtained averages of only about 3 per cent. 

Gesell 1 has claimed that in children there is a high positive 
correlation amongst individuals between accuracy of handwrit- 
ing and intellectual ability. His own data, however, really show 
a correlation of only about .3, and it seems probable that what 






1 Accuracy in Handwriting, as Related to School Intelligence and Sex. 
Am. Jour, of Psy. Vol. 17, pp. 394-405- 



The Speed and Quality of Handwriting 39 

correlation there is is due in large measure to the greater zeal of 
the brighter pupils to excel in all respects, rather than to any fun- 
damental close correspondence of intellect with motor ability. 
The records of our adults add to the evidence that ability in 
thought and ability in movements are, in adults, only very slightly 
related. The correlation between scholarship grade and quality 
of handwriting is zero. For 21 individuals taken at random from 
the best third of the writers, the median grade in scholarship was 
about exactly C +. For 22 individuals taken at random from 
the worst third in writing the median grade in scholarship was a 
little above B — •, 

Legibility as a Factor in the Quality of Handwriting 

Legibility is a word with many possible meanings. In one 
of its meanings the legibility of writing may be measured by the 
distance at which it can be read with a given accuracy and rate. 
In another of its meanings it can be measured by the rate at 
which a sample can be read at a given distance and with a given 
accuracy. Still finer discrimination might perhaps be made be- 
tween samples of handwriting equally legible by these two tests, 
by a further test of the degree of fatigue or of discomfort re- 
sulting from reading them. Even the subjective measurement 
of legibility by the combined opinions of competent judges is 
useful. 

Legibility may be tested in any one of these ways in the case 
of single letters or groups of letters cut from a sample, of words 
alone or in a random order, and in the case of words in a sensible 
context where what is before and after the word helps one to 
read it. Also, legibility for a tyro at reading and for a trained 
reader may well be different things, requiring separate investiga- 
tion. 

I have made rough measurements of the legibility of the dif- 
ferent qualities of the scales for children's and adults' writing, 
but the results are too meagre for publication at this time. They 
show, as might be foreseen, that the higher grades of quality 
differ little in the legibility of the words in a context for a 
trained reader, but correlate fairly closely with the legibility of 
the letters singly. 



40 Handwriting 

Section 14. A Scale of Children's Writing, Based on Equally 
Often Noted Differences in Quality 

In section 2 the fact was noted that a series of samples, a, b, 
c, d, etc., could be found such that when each was compared 
with the others a was judged better than b as often as b was 
judged better than c, and so on. It was pointed out that, if the 
per cents of judgments of a-b, b-c } etc., are under 100, over 50, 
and equal, the samples a, b, c } etc., may be regarded as differing 
by equal steps, equal differences meaning equally often noticed 
differences. A scale constructed on this principle differs from 
one constructed on the principle that differences judged equal 
by the combined opinion of competent judges are equal, chiefly 
in respect to the lower qualities of handwriting. The difference 
between lower qualities that is noticed as often as a given dif- 
ference between higher qualities is regarded by competent judges 
as a smaller difference than the latter. 

The reasons for this are interesting and the general problem 
of the choice between " judged equal " and " noticed equally 
often " as the basis for equality of units in psychological, educa- 
tional and sociological scales is of very great importance. But 
much more elaborate investigations than I have been able to 
make are necessary for any adequate discussion of the problem, 
even in the case of handwriting alone. 

I therefore simply present the scale as derived by this second 
method for the use of those who prefer it. The facts are that : 

Sample 125 is, in direct comparison with sample 132, judged to be 
better by 81 per cent of 42 judges. 

132 is similarly judged better than 58 by 81% of 42 judges 

58 " " " 10 by 79% 

10 " " " 1 by 79% 

1 " " " 55 by 79% 

55 " " " 52 by 77% 91 

52 " " " 44 by 83.5% " 

44 " " " 34 by 79% 

34 " " " 51 by 78% 

51 " " " 22 by 80% 

22 " " " 126 by 74% 42 

Samples 126, 22, 51, 34, 44, 52, and so on, thus have approxi- 
mately the values x, x + k, x + 2k, x + 3&, x + 4k, respectively, 
where ;r — the difference in quality between sample 126 and zero 



The Speed and Quality of Handwriting 41 

quality, and k = such a difference in quality as is noted as dif- 
ferent by competent judges eight times out of ten. K is, on the 
average, equal to 1 of steps 7 to 17 of scale A, but the value of 
x remains undetermined. If a series was found ranging from 
a sample arbitrarily taken as of zero merit (say, sample 140) to 
sample 126, such that the difference between any two successive 
samples was noted eight times out of ten, the number of steps 
in this series would give the value of x in terms of k. X is 
probably between 8k and gk. Since, however, the calculation 
of the distance of x from by other methods worthy of con- 
sideration makes it as low as 6k or even $k, I shall use jk as 
the distance of sample 126 from 0. Anyone preferring to adhere 
rigidly to " noticed equally often " as the sole test of equality 
of difference may use 19.5, 18.5, 17.5, 16.5, etc., in place of the 
18, 17, 16, 15, etc., used in the scale. 



HANDWRITIN^ 



By EDWARD L. THORNDIKE 

Professor of Educational Psychology, Teachers College 
Columbia University 



PUBLISHED BY 

Cfeadynrfl (EaUpgp, OIntombta Uttiwraitg 

NEW YORK CITY 

1912 



